The Exchange Rate and Purchasing Power Parity in Arbitrage-Free Models of Asset Pricing

Assuming that asset markets are complete and arbitrage-free, the exchange rate can be expressed in terms of observables in a multicountry, multigood general equilibrium economy. In contrast to existing models of the exchange rate, this general model allows for international differences in consumption preferences, time preferences, and the degree of risk aversion, and does not need to specify the imperfections in commodity markets. Changes in the equilibrium exchange rate are given by international differences in: (i) inflation rates computed from marginal spending weights, (ii) growth rates of real spending, weighted by the countries' measures of relative risk-aversion, and (iii) subjective discount rates. The discount rates and risk aversions can vary both over time and across countries. In this general framework, relative Purchasing Power Parity (PPP) holds only if preferences are homothetic and, either (a) investors are risk neutral or (b) commodity markets are perfect and preferences are identical across countries; in all other cases, CPI inflation is only one of the factors determining exchange rate changes. Thus, compared to this general model for exchange rates, standard regression and cointegration tests of PPP suffer from missing-variables biases, errors-in-variables biases, and ignore variations in risk aversions across countries and over time. An attractive feature of this model is that it nests several existing equilibrium models of the exchange rate and also PPP, thus providing a theoretical framework to distinguish empirically between these models. When estimating this equation as a long-run relationship, Sercu and Uppal (2000) and Apte, Sercu and Uppal (2006) find significant evidence against long-run PPP and largely supportive evidence in favor of the more general model.